This allows us to visualize the mapping of keys from one layout to another:

1

KeyGraph[dvorak, qwerty]

There is a single directed edge going from each character to the one that will be displayed when you type it. There are 3 keys that remain unchanged, 2 pairs of swapped keys, and 2 large cycles of keys.

It will take the length of the cycle the letter is in to get the letter we want. For a given word, we won’t get all the letters we want unless we’ve iterated some multiple of the length of the cycles each letter is in. Let’s apply the Least Common Multiple function to see the worst case where there is a letter from each cycle:

1234

LCM@@Length/@ConnectedComponents@KeyGraph[dvorak, qwerty]

Output

1

210

Looks like Anna got lucky that her name only consists of letters in a cycle of length 1 and 15.